Finite Group Databasebeta

← #135×D313 #34094930

Subgroups — #135×D313 #34094930

Order 20032.

266 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×D313C212yesmaximal, complemented
2#23756520C211yesmaximal, characteristic, complemented
3#23756519C211yesmaximal, characteristic, complemented
4#23756518C212yesmaximal, complemented
5#23756517C212yesmaximal, complemented
6#23756516C211yesmaximal, characteristic, complemented
7Q16×D313C211yesmaximal, characteristic, complemented
8SD16×D313C212yesmaximal, complemented
9D8×D313C211yesmaximal, characteristic, complemented
10C2×C8×D313C211yesmaximal, characteristic, complemented
11#135×C313C211yesmaximal, characteristic, complemented
12#19097562C2212yescomplemented
13#19097561—22no—
14#19097561C2212yescomplemented
15#19097560—22no—
16#19097560C2212yescomplemented
17Q8×D313C2212yes—
18D4×D313—22no—
19D4×D313C2212yes—
20C2×C4×D313—22no—
21C2×C4×D313C2211yescharacteristic
22Dic1252C2211yescharacteristic, complemented
23#19097551C2212yescomplemented
24#19097550C2212yescomplemented
25#19097549C2212yescomplemented
26#19097548C2212yescomplemented
27D2504C2211yescharacteristic, complemented
28#19097546C2212yescomplemented
29C2×#14578809C2211yescharacteristic, complemented
30C8×D313C2211yescharacteristic
31C8×D313C2211yescharacteristic
32C8×D313C2211yescharacteristic, complemented
33C8×D313C2211yescharacteristic, complemented
34#41×C313C2212yescomplemented
35Q16×C313C2211yescharacteristic, complemented
36SD16×C313C2212yescomplemented
37D8×C313C2211yescharacteristic, complemented
38C2×C8×C313C2211yescharacteristic, complemented
39C22×D313—22no—
40C22×D313D411yescharacteristic
41Dic626—22no—
42Dic626C2312yes—
43D1252—22no—
44D1252C2312yes—
45C22⋊D313—22no—
46C22⋊D313—22no—
47C22⋊D313—22no—
48C2×Dic313—22no—
49C2×Dic313D411yescharacteristic
50C4×D313—22no—
51C4×D313—22no—
52C4×D313—22no—
53C4×D313D411yescharacteristic
54C4×D313D411yescharacteristic
55C4×D313C2311yescharacteristic
56C4×D313C2311yescharacteristic
57#14578809C2311yescharacteristic
58#14578809C2311yescharacteristic
59Q8×C313C2312yes—
60D4×C313—22no—
61D4×C313C2312yes—
62C2×C4×C313—22no—
63C2×C4×C313C2311yescharacteristic
64C8×C313C2311yescharacteristic
65C8×C313C2311yescharacteristic
66C22×C313—22no—
67C22×C313C2×D411yescharacteristic
68C2×D313—22no—
69C2×D313—22no—
70C2×D313—44no—
71C2×D313C2×D411yescharacteristic
72C2×D313C2×D411yescharacteristic
73C4×C313—22no—
74C4×C313C2×D411yescharacteristic
75C4×C313C2411yescharacteristic
76Dic313—22no—
77Dic313C2×D411yescharacteristic
78Dic313C2×D411yescharacteristic
79C2×C313—21no—
80C2×C313—42no—
81C2×C313C22×D411yescharacteristic
82D313—21no—
83D313—42no—
84D313#13512yesdirect product factor
85C313C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—3131nomaximal, Sylow
87C2×#41—3132no—
88#135—3132no—
89#135—3131no—
90#135—3132no—
91#135—3131no—
92#135—3131no—
93#135D31311yescharacteristic, direct product factor
94C2×Q16—3131no—
95C2×SD16—3132no—
96C2×D8—3131no—
97C22×C8—3131no—
98#41—3132no—
99#41—3132no—
100#41—3132no—
101#41—6262no—
102#41—6262no—
103#41C2×D31312yescomplemented
104C2×Q8—3132no—
105C2×D4—3132no—
106C2×D4—6262no—
107C22×C4—3131no—
108C22×C4—6262no—
109Q16—3132no—
110Q16—3131no—
111Q16C2×D31311yescharacteristic, complemented
112SD16—3132no—
113SD16—3132no—
114SD16—3132no—
115SD16C2×D31312yescomplemented
116D8—3132no—
117D8—3131no—
118D8C2×D31311yescharacteristic, complemented
119C2×C8—3131no—
120C2×C8—3131no—
121C2×C8—3131no—
122C2×C8—3131no—
123C2×C8—3131no—
124C2×C8C2×D31311yescharacteristic, complemented
125C23—3131no—
126C23—6262no—
127Q8—3132no—
128Q8—6262no—
129Q8C22×D31312yes—
130D4—22no—
131D4—3132no—
132D4—6262no—
133D4—6262no—
134D4—6262no—
135D4—6262no—
136D4C22×D31312yes—
137C2×C4—22no—
138C2×C4—3131no—
139C2×C4—3131no—
140C2×C4—3131no—
141C2×C4—3131no—
142C2×C4—3131no—
143C2×C4—6262no—
144C2×C4—6262no—
145C2×C4—6262no—
146C2×C4—6262no—
147C2×C4C22×D31311yescharacteristic
148C8—3131no—
149C8—3131no—
150C8C22×D31311yescharacteristic
151C8C22×D31311yescharacteristic
152C22—22no—
153C22—3131no—
154C22—3131no—
155C22—6262no—
156C22—6262no—
157C22—12524no—
158C22D4×D31311yescharacteristic
159C4—22no—
160C4—3131no—
161C4—3131no—
162C4—6262no—
163C4D4×D31311yescharacteristic
164C4C23×D31311yescharacteristic
165C2—21no—
166C2—42no—
167C2—3132no—
168C2—6261no—
169C2—12522no—
170C2C2×D4×D31311yescharacteristic
subgroupG/H
centerC4D4×D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
Fitting#135×C313C2
socleC2×C313C22×D4
hypercenter#135D313
hypocenterC313C2×#135
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #41×D313C2semidirect
2. #23756520C2semidirect
3. #23756519C2semidirect
4. #23756518C2semidirect
5. #23756517C2semidirect
6. #23756516C2semidirect
7. Q16×D313C2semidirect
8. SD16×D313C2semidirect
9. D8×D313C2semidirect
10. C2×C8×D313C2semidirect
11. #135×C313C2semidirect
12. #19097562C22semidirect
14. #19097561C22semidirect
16. #19097560C22semidirect
22. Dic1252C22semidirect
23. #19097551C22semidirect
24. #19097550C22semidirect
25. #19097549C22semidirect
26. #19097548C22semidirect
27. D2504C22semidirect
28. #19097546C22semidirect
29. C2×#14578809C22semidirect
32. C8×D313C22semidirect
33. C8×D313C22semidirect
34. #41×C313C22semidirect
35. Q16×C313C22semidirect
36. SD16×C313C22semidirect
37. D8×C313C22semidirect
38. C2×C8×C313C22semidirect
84. D313#135direct (N × H)
85. C313C2×#135semidirect
93. #135D313direct (N × H)
103. #41C2×D313semidirect
111. Q16C2×D313semidirect
115. SD16C2×D313semidirect
118. D8C2×D313semidirect
124. C2×C8C2×D313semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#41×D3132
#237565202
#237565192
#237565182
#237565172
#237565162
Q16×D3132
SD16×D3132
D8×D3132
C2×C8×D3132
#135×C3132
C2×#135313